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Large edge localised modes (ELMs) would cause an unacceptable reduction of material lifetime in future large tokamaks due to the significant amount of energy expelled from the magnetically confined region towards the plasma facing components. Thoroughly validated modelling of regimes devoid of large ELMs is crucial as it may then provide predictive insights prior to tokamak operation and design. This paper describes recent efforts pursued with the non-linear extended MHD code JOREK in the modelling of three scenarios without large ELMs: quiescent H-mode (QH-mode), quasi-continuous exhaust regime (QCE regime), and the enhanced D-alpha H-mode (EDA H-mode). For each of these regimes, the non-linear dynamics observed in the simulations are detailed and compared to experimental observations of the underlying instabilities of each regime (edge harmonic oscillation for QH-mode, small ELMs for QCE regime, and quasi-coherent mode for EDA H-mode). For QH-mode, the kink-peeling mode is found to govern the dynamics and a transition to a large ELM is obtained above the same density threshold as in the modelled experiment. For the QCE regime and EDA H-mode, resistive peeling–ballooning modes dominate and pedestal fluctuation frequencies correspond well to experimental observations. The dominant mechanisms for the excitation and suppression of these instabilities are presented and their influence on simulation dynamics is shown. Finally, predictive simulations of edge instabilities at different values of plasma resistivity in a 4.60 MA scenario with low edge safety factor in JT-60SA are presented.